Patients receive melphalan IV over 15 minutes on day -1. Autologous peripheral blood stem cells (PBSCs) are reinfused on day 0. Patients also receive sargramostim (GM-CSF) subcutaneously (SC) or IV over at least 30 minutes daily beginning on day 1 and continuing until blood counts recover. Beginning 100-182 days after autologous PBSC transplantation, patients receive fludarabine IV over 30 minutes on days -6 to -2 and cyclophosphamide IV over 1-2 hours on days -3 and -2. Allogeneic PBSCs are infused on day 0. Patients may receive a second allogeneic PBSC infusion on day 1. Patients also receive GM-CSF SC or IV over at least 30 minutes daily beginning on day 1 and continuing until blood counts recover. Cyclosporine is administered IV or orally twice daily as graft-versus-host disease (GVHD) prophylaxis, beginning on day -1 and continuing until day 60, followed by a taper in the absence of GVHD.